whicbrings us back to the alhamb, with its surfaces covered in repeating geometric motifs, beautifully integrated with poetry carved into the walls: "you will say upon seeing it: it is a fortress, and at the same time, a mansion of happiness. it is a dwelling for the peaceful and the warrior. it is an artistic work that produces wisdom." whether the islamic designers of the alhambra understood the mathematics of symmetry and how is a matter of conjecture. what we do know is that the work of islamic mathematicians in spatial symmetry and algebra foreshadowed the creation of group theory, a core concept of symmetry. the study of symmetry allows us to look at geometric things using algebraic tools. and that lets us both solve difficult problems and connect things that don't seem to have anything to do with each other. how? it's all about symmetry groups and something called invariance. so symmetry, group theory, the math of beauty, actually, is what it is, is ultimately a lot of algebra, and so we're lucky to have with us today rosa orellana, professor of mathematics at dartmouth college,